Differential Equation Models.

Includes Index

Modules in Applied Mathematics: Volume 1; Editor's page ; Copyright; Preface; Preface for Volume 1; Contents; Contents for the Companion Volumes; PART I DIFFERENTIAL EQUATIONS, MODELS, AND WHAT TO DO WITH THEM; CHAPTER 1 Setting Up First-Order Differential Equations from Word Problems; CHAPTER 2 Qualitative Solution Sketching for First-Order Differential Equations; CHAPTER 3 Difference and Differential Equation Population Growth Models; PART II GROWTH AND DECAY MODELS: FIRST-ORDER DIFFERENTIAL EQUATIONS; CHAPTER 4 The Van Meegeren Art Forgeries; CHAPTER 5 Single Species Population Models. CHAPTER 6 The Spread of Technological InnovationsPART III HIGHER ORDER LINEAR MODELS; CHAPTER 7 A Model for the Detection of Diabetes; CHAPTER 8 Combat Models; CHAPTER 9 Modeling Linear Systems by Frequency Response Methods; PART IV TRAFFIC MODELS; CHAPTER 10 How Long Should a Traffic Light Remain Amber?; CHAPTER 11 Queue Length at a Traffic Light via Flow Theory; CHAPTER 12 Car-Following Models; CHAPTER 13 Equilibrium Speed Distributions; CHAPTER 14 Traffic Flow Theory; PART V INTERACTING SPECIES: STEADY STATES OF NONLINEAR SYSTEMS. CHAPTER 15 Why the Percentage of Sharks Caught in the Mediterranean Sea Rose Dramatically during World War ICHAPTER 16 Quadratic Population Models: Almost Never Any Cycles; CHAPTER 17 The Principle of Competitive Exclusion in Population Biology; CHAPTER 18 Biological Cycles and the Fivefold Way; CHAPTER 19 Hilbert's 16th Problem: How Many Cycles?; PART VI MODELS LEADING TO PARTIAL DIFFERENTIAL EQUATIONS; CHAPTER 20 Surge Tank Analysis; CHAPTER 21 Shaking a Piece of String to Rest; CHAPTER 22 Heat Transfer in Frozen Soil; CHAPTER 23 Network Analysis of Steam Generator Flow.

The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.